Overview
On this page, we discuss how to solve equations of the form \(ax^k + b = 0\) by applying the \(k^{\text{th}}\) root, and how to solve general quadratic equations of the form \(ax^2 + bx + c = 0\) with the quadratic formula.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Solve an equation where the variable appears in a single term, under a power, by isolating that term and rooting both sides.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Solve an equation of the form \(ax^2 + bx + c = 0\) with the quadratic formula.
- Understand how to use the discriminant, \(\Delta = b^2 - 4ac\) to determine how many solutions the equation \(ax^2 + bx + c = 0\) has.
To prepare for class
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Watch the following videos (by Tyler Wallace) which show how to solve equations where the variable appears in a single term, under a power:
After class
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Watch the following videos (by Tyler Wallace) which give examples of how to use the quadratic formula:
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Watch the following video (by Tyler Wallace) which gives the derivation of the quadratic formula:
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Watch the following video (by patrickJMT) which shows an example of quickly determining the number of solitions to a quadratic equation by computing the discriminant:
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Watch the following video (by Veritasium) which shows how to complete the square geometrically, and outlines the history of solving quadratic and cubic equations: